Interpretation theoretical moments 2nd order approximation

Hi there,

when I set up a model in levels so that I can do a 2nd order approximation, do the theoretical moments have a meaning? E.g. when I get a negative mean for the inflation rate, could this be interpreted that there will be deflation on average/in steady state? Or since a 2nd order approximation does include all these co-variance terms, there is no economic interpretation for these theoretical means when doing a 2nd order approximation?

I will be very grateful if you can help me out with this

As shown in e.g. Schmitt-Grohe/Uribe (2004): “Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function”, you get an additional constant term that corrects the deterministic steady state for the presence of risk. This term has an economic meaning/interpretation. So when the theoretical mean for inflation at second order is negative, the model indeed predicts deflation on average.